Abstract
Numerical studies of Ising square lattices with random bonds (Jij =±J or drawn from a gaussian distribution) are reviewed. Particular attention is paid to the temperature- and field dependence of the equilibrium magnetization M(H,T). While for a symmetric bond distribution the zero-field susceptibility trivially follows a Curies law Xo∝ T−1, the nonlinear susceptibility Xn ℓ shows a dramatic temperature-dependence, which can nearly be mistaken for a power-law divergence at a freezing temperature Tf. These findings are compared in detail with corresponding experimental data, including possible “scaling” representations. We relate this behavior to the onset of long-range Edwards-Anderson order as T→0, as measured by the correlation function gEA(rij)=[<SiSj> 2T ]av
We then discuss time-dependent quantities: the spin-spin autocorrelation function and the time-dependent Edwards-Anderson order parameter q(t), dynamic susceptibility χ(t) etc.; also the onset of irreversible behavior at critical magnetic fields Hc(t) is emphasized, and again compared to experiments. A possible explanation of this behavior in terms of the free energy barriers separating the various “valleys” in configuration space is indicated.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
L. Néel, Ann. Geophys. l5, 99 (1949)
J.L. Tholence and R. Tournier, J. Phys. (Paris) 35, C4–229 (1974)
J.L. Tholence, J. Appl. Phys. 50, 7310 (1979); Solid State Comm. 35, 113 (1980)
E.P. Wohlfarth, Physica 86-88B, 852 (1977); J. Phys. F10, 1,241 (1980); Phys. Lett. 70A, 489 (1979); E.P. Wohlfarth and S. Shtrikman, Phys. Lett. 85A, 467 (1981)
M. Gyrot, Solid State Comm. 39, 1009 (1981)
For a review, see J.A. Mydosh, J. Mag. Magn. Mat. 7, 237 (1978)
G. Eiselt, J. Kötzler, H. Maletta, D. Stauffer and K. Binder, Phys. Rev. B19, 2664 (1979)
S.F. Edwards and P.W. Anderson, J. Phys. F5, 965 (1975)
D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975)
G. Parisi, J. Phys. A13, L115 (1980); Phil. Mag. B41,677 (1980)
H. Sompolinsky, Phys. Rev. Lett. 47, 935 (1981); H. Sompolinsky and A. Zippelius, Phys. Rev. B25, 6860 (1982); J. Hertz, J. Phys. C16, 1219 (1983); 1233 (1983)
A.P. Young, J. Phys. C14, L1085 (1981); A.P. Young and S. Kirkpatrick, Phys. Rev. B25, 440 (1982); A. Houghton, S. Jain and A.P. Young, preprint; N.D. Mackenzie and A.P. Young, Phys. Rev. Lett. 49, 301 (1982), and preprint; A.P. Young and C. de Dominicis, preprint
R.G. Palmer, Adv. Phys. 31, 669 (1982)
J.R.L. De Almeida and D.J. Thouless, J. Phys. A11, 983 (1978)
G. Parisi and G. Thouless, J. Phys. Lett. (Paris) 41, L361 (1980); G. Toulouse, M. Gabay, T.C. Lubensky and J. Vannimenus, J. Phys. Lett. 43, L109 (1982)
M.E. Fisher, Rev. Modern Phys. 46, 597 (1974)
A.B. Harris, T.C. Lubensky, and J.H. Chen, Phys. Rev. Lett. 38, 765 (1976)
R. Fisch and A.B. Harris, Phys. Rev. Lett. 38, 785 (1977)
A.J. Bray and M.A. Moore, J. Phys. F7, L333 (1977); A.J. Bray, M.A. Moore, and P. Reed, J. Phys. C11, 1187 (1978)
A.J. Bray and M.A. Moore, Phys. Rev. Lett. 41, 1068 (1978); J. Phys. C12, 1,441 (1979); see also H. Sompolinsky and A. Zippelius, Phys. Rev. Lett. 50,1294 (1983)
I. Morgenstern and K. Binder, Phys. Rev. Lett. 43, 1615 (1979); Phys. Rev. B22, 288 (1980)
I. Morgenstern and K. Binder, Z. Phys. B39, 227 (1980)
J.R. Banavar and M. Cieplak, Phys. Rev. Lett. 82, 832 (1982)
W. Kinzel and K.H. Fischer, J. Phys. C11, 2115 (1978), and references therein
P.W. Anderson and C.W. Pand, Phys. Rev. Lett. 40, 903 (1978)
D. Stauffer and K. Binder, Z. Physik B30, 313 (1978); B34, 97 (1979)
L. Lundgren, P. Svedlindh, and O. Beckmann, Phys. Rev. B26, 3990 (1982)
P. Monod and H. Bouchiat, J. Phys. Lett. (Paris) 43, L45 (1982)
B. Barbara, A.P. Malozemoff, and Y. Imry, Phys. Rev. Lett. 47, 1852 (1981); A.P. Malozemoff, B. Barbara, and Y. Impry, J. Appl. Phys. 53, 2205 (1982)
B. Barbara, A.P. Malozemoff, and Y. Imry, Physica 108B+C, 1289 (1981)
A. Berton, J. Chaussy, J. Odin, B. Rammal, and R. Tournier, J. Phys. Lett.(Pais) 43, L–153 (1982)
R. Omari, J.J. Prejean, and J. Souletie, J. phys. (Paris) in press
J. Ferré, J. Rajchenbach and H. Maletta, J. Appl. Phys. 52, 1967 (1981)
M. Guyot, S. Foner, S.K. Hasanain, R.P. Guertin, and K. Westerhold, Phys. Lett. 79A, 339 (1980)
MB. Salamon, K.V. Rav, and Y. Yeshurun, J. Appl. Phys. 52, 1687 (1981)
R.V. Chamberlin, M. Hardiman, L.A. Turkevich and R. Orbach, Phys. Rev. B25, 6720 (1982)
Y. Yeshurun and H. Sompolinsky, Phys. Rev. B26, 1487 (1982)
N. Bontemps, J. Rajchenbach, and R. Orbach, J. Phys. Lett. (Paris) 44, L47 (1983)
M.B. Salamon, and J.L. Tholence, J. Appl. Phys. 53, 7684 (1982); J. Magn. Mag. Mat., in press
J. Hamida, C. Paulsen, S.J. Williamson, and H. Maletta, preprint
K. Binder and K. Schröder, Phys. Rev. B14, 2142 (1976)
K. Binder, Z. Phys. B26, 339 (1977)
W. Kinzel, Phys. Rev. B19, 4594 (1979)
K. Binder and D. Stauffer, Phys. Lett. 57A, 177 (1976)
Note that finite energy barriers between different ground states need not rule out a phase transition, see P. Hoever, W.F. Wolff, and J. Zittartz, Z. Phys. B41, 43 (1981); B42, 259 (1981); P. Hoever and J. Zittartz, Z. Phys. B44, 129 (1981)
I. Morgenstern, J. Appl. Phys. 53, 7682 (1982); Phys. Rev. B27, 4522 (1983); see also I. Morgenstern, and H. Horner, Phys. Rev. B25, 504 (1982)
W. Kinzel, Z. Phys. B46, 59 (1982)
W. Kinzel, Phys. Rev. B26, 6303 (1982)
K. Binder and I. Morgenstern, Phys. Rev. B27, 5826 (1983)
K. Binder, Z. Phys. B48, 319 (1982)
A.P. Young, Phys. Rev Lett. 50, 917 (1983)
W. Kinzel and K. Binder, Phys-Rev. Lett. 50, 1509 (1983); and to be published
K. Binder and D. Stauffer, in Monte Carlo Methods in Statistical Physics (K. Binder, ed., Springer, Berlin 1979) p.301; K. Binder, J. Phys. (Paris) 39, C61527 (1978); K. Binder, in Ordering in Strongly Fluctuating Condensed Matter Systems (T. Riste, ed., Plenum Press, New York 1979) p.423; K. Binder and D. Stauffer, in Monte Carlo Methods in Statistical Physics II (K. Binder, ed., Springer, to be published).
H. Hilhorst and B. Derrida, J. Phys. C14, L539 (1981)
J.L. van Hemmen and I. Morgenstern, J. Phys. C15, 4353 (1982)
J.A. Mydosh, J. Phys.Soc. Jpn. 52, Suppl. p.85 (1983)
P.C. Hohenberg and B.I.Halperin, Rev. Mod. Phys. 49, 435 (1977)
I. Morgenstern, Phys. Rev. B25, 6067 (1982)
H. Maletta, J. Phys. (Paris) C6, 115 (1980), and references therein
B. Barbara, and A.P. Malozemoff, Proc. 16th Rare Earth Research Conf., Florida State Univ., April 1983 to be published
It should be noted that the physical significance of the shift of the susceptibility maximum at very small fields can be questioned on a various physical grounds: (i) it may be an artefact due to macroscopic sample inhomogeneities (H. Alloul, private communication) (ii) it may be an effect specific for Heisenberg spins, just as there exists for isotropic Heisenberg antiferromagnets in a field a cuspshaped umbilicus of the critical temperatures.Tc(H),Tc(-H), which merge at the T-axis in a bicritical point (G. Toulouse, private communication). In Ising spin glasses for d<dℓ none of these alternative explanations can apply, however.
These data were obtained in [41] by stepwise decrease of H at constant T, and thus for small H near Tf are slightly affected by observation time effects. The scaling analysis of Sec.IV hence uses more accurate recent simulation data [52] obtained by field-cooling as in Figs.1,2.
J. Chalupa, Solid State Commun. 24, 429 (1977); M. Suzuki, Progr. Theor. Phys. 58, 1151 (1977); K. Binder, Festkörperprobleme 17, 55 (1977)
N. Bontemps and J. Rajchenbach, to be published
K. Binder and W. Kinzel, in Lecture Notes in Physics 149, p.124 (ed. by C. di Castro) Springer Berlin, Heidelberg and New York, 1981.
F. Mezei, in Recent Developments in Condensed Matter Physics ed. J.T. Devreese (Plenum, Press, New York 1981) Vol.l, p.679
D. Hüser, L.E. Wenger, A.J. van Duyneveldt and J.A. Mydosh, Phys. Rev. B, in press
D.E. Mac Laughlin, L.C. Gupta, R.H. Heffner, M. Leon, and M.E. Schillaci, to be published
A.P. Malozemoff and Y. Imry: Phys. Rev. B24, 489 (1981)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
Binder, K., Kinzel, W. (1983). The spin glass transition: a comparison of Monte Carlo simulations of nearest-neighbor Ising Edwards-Anderson models with experiments. In: van Hemmen, J.L., Morgenstern, I. (eds) Heidelberg Colloquium on Spin Glasses. Lecture Notes in Physics, vol 192. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12872-7_54
Download citation
DOI: https://doi.org/10.1007/3-540-12872-7_54
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12872-4
Online ISBN: 978-3-540-38761-9
eBook Packages: Springer Book Archive